1. Field of the Invention
This invention relates to a system and method for reducing non-linear electrical distortion in an electroacoustic device. Specifically, the present invention relates to a system and method for reducing spatially dependent electrical distortion, for example, distortion caused by differences in electrical displacement between a conductive membrane and a counter electrode at different parts of the conductive membrane. The system and method for reducing non-linear electrical distortion has particular application in condenser microphones comprising, for example, a conductive diaphragm receptive to sound, and a backplate electrically coupled thereto to generate an electrical output.
2. Description of Related Art
Generally, an electroacoustic device such as, for example, a condenser microphone, converts sound pressure input into electrical output.
FIG. 1 illustrates an example of a condenser microphone system 10. The microphone 10 comprises a conductive membrane 12 exposed to sound 24, electrically coupled to a counter electrode 14. A conductive membrane 12 may be, for example, a diaphragm. Examples of counter electrodes include a back electrode, a backplate, and a conductive front grille. Generally, the counter electrode 14 is stationary and displaced in parallel and in close proximity to the conductive membrane 12, such that the combination of the electrode 14 and membrane 12 acts as a capacitor capable of storing a charge. A polarizing voltage, Eo, is applied either through a polarizing voltage source 16 and polarization resistor 18, or by using an electric layer (not shown), by which a constant initial charge is established. This constant initial charge provides initial voltage when the diaphragm 12 is not affected by sound waves 24, that is, when the diaphragm 12 is in a rest position. Additionally, the exemplary condenser microphone 10 may include one or more parasitic parallel load capacitors 20 and a preamplifier section 22 to produce an amplified electrical output 26.
When sound impinges on the membrane 12, it moves, thus changing capacitance between itself and the counter electrode. This produces a variable voltage, which is the electrical output signal, E. In an ideal electroacoustic system, the electrical output, E, varies linearly with the pressure of actuating sound waves 24 upon the membrane 12. A linear movement/output voltage relationship means that the diaphragm 12 maintains a parallel relationship with the counter electrode 14. This assumes, in the ideal case, that displacement due to a given sound pressure is in a direction perpendicular to the parallel relationship and equal in magnitude at all areas of the diaphragm 12.
FIG. 2 illustrates the parallel displacement, d, of the diaphragm 28 in relation to counter electrode 30 in an ideal system 27. Assuming, for simplicity, that no parasitic parallel load capacitances exist,             C      a        =                  C        0            /              (                  1          +                      d            /            D                          )              ,            and      ⁢              xe2x80x83            ⁢      E        =                            E          0                ⁢                              C            0                                C            a                              =                        E          0                ⁡                  (                      1            +                          d              /              D                                )                      ,  where
Ca is the active capacitance (varies with diaphragm displacement),
C0 is the capacitance at rest position,
d is the displacement of membrane with sound pressure,
D is the rest distance between counter electrode and diaphragm,
E is the output voltage (constitutes signal), and
E0 is the polarization voltage (voltage at rest position).
Therefore, in an ideal system, the output voltage varies linearly with the displacement between diaphragm 28 and counter electrode 30. However, in a typical electroacoustic system, the relationship between electrical output, E, and sound pressure is non linear.
FIG. 3 illustrates a typical system 31, comprising a flexible diaphragm 32, stretched and clamped at its edges. The particular tension of the diaphragm and the method of attaching are well understood in the art, and are not important for an understanding of the present invention. The displacement of the diaphragm 32 to sound at frequencies below resonance is parabolic, such that an equal distance between the diaphragm 32 and counter electrode 34 is not maintained from all areas of the diaphragm 32. For example, D/d(r1) is not equal to D/d(r2). Therefore, the change of capacitance between diaphragm 32 and counter electrode 34 is spatially dependent. This spatial dependence manifests itself as a signal dependant stray capacitance which makes active capacitance, Ca, nonlinear. It has been shown that the displacement of such a diaphragm may be represented by d(r)=d0(1xe2x88x92r2/Rd2), where
rxe2x80x94radial coordinate with its origin at the center of the diaphragm,
Rdxe2x80x94radius of the diaphragm
d0xe2x80x94diaphragm displacement at the center.
The initial capacitance between the diaphragm 32 and counter electrode 34, that is, the capacitance without displacement of the diaphragm 32, may be represented by,       C    0    =                    ϵ        ·        π        ·                  R          b          2                    D        .  
Then, the active capacitance, Ca, and output voltage, E, may be represented by             C      a        =                            ∫          0                      R            b                          ⁢                                                            ϵ                ·                2                            ⁢                              π                ·                r                                                    D              +                                                d                  0                                ⁢                                  (                                      1                    -                                                                  r                        2                                            /                                              R                        d                        2                                                                              )                                                              ⁢                      xe2x80x83                    ⁢                      ⅆ            r                              =                                                                  ϵ                ·                2                            ⁢                              π                ·                                  R                  b                  2                                                                    D              ·                              R                b                2                                              ⁢                                    ∫              0                              R                b                                      ⁢                                                            2                  ⁢                  r                                                  1                  +                                                                                    d                        0                                            D                                        ⁢                                          (                                              1                        -                                                                              r                            2                                                    /                                                      R                            d                            2                                                                                              )                                                                                  ⁢                              ⅆ                r                                                    =                                            C              0                        ·                                          R                d                2                                            R                b                2                                      ·                          D                              d                0                                      ·            ln                    ⁢                                    1              +                                                d                  0                                /                D                                                    1              +                                                (                                      1                    -                                                                  R                        b                        2                                            /                                              R                        d                        2                                                                              )                                ·                                                      d                    0                                    /                  D                                                                          ,
and       E    =                            E          0                ⁢                              C            0                                C            a                              =                        E          0                ·                              R            b            2                                R            d            2                          ·                              d            0                    D                ·                  1                      ln            ⁢                                          1                +                                                      d                    0                                    /                  D                                                            1                +                                                      (                                          1                      -                                                                        R                          b                          2                                                /                                                  R                          d                          2                                                                                      )                                    ·                                                            d                      0                                        /                    D                                                                                            ,
where
Rb is the radius of the counter electrode.
As the equation for E shows, the relationship between the output voltage E and diaphragm displacement is non-linear.
FIG. 4 provides a graph 36 illustrating the non-linearity of the relationship between the output voltage and diaphragm displacement in a typical system 38 as compared to the linear relationship in an ideal system 40. The problem lies in the fact that the ratio of the motion to the distance to the counter electrode is different for different areas of the diaphragm 32.
The present invention provides a system and method for reducing variations in electrical displacement between different sections of a conductive membrane and a counter electrode electrically coupled to the conductive membrane in an electroacoustic device.
One embodiment of the present invention provides a system comprising a counter electrode, a face of which faces the conductive membrane and is curved to minimize the variations in electrical displacement between different sections of the conductive membrane and the counter electrode.
In another embodiment, the counter electrode is variably polarized to counteract for variations in displacement across the conductive membrane. In yet another embodiment, the diaphragm is variably polarized for this purpose.
In an alternative embodiment, the present invention provides a system comprising a translational apparatus for translating a rigid conductive membrane laterally to maintain its parallel relationship to the counter electrode during reverberations.
It will be appreciated by those skilled in the art that although the following Detailed Description will proceed with reference being made to exemplary embodiments and methods of use, the present invention is not intended to be limited to these exemplary embodiments and methods of use. Rather, the present invention is intended to be limited only as set forth in the accompanying claims.